Pre-Algebra Examples

$y = 0.25 x + 25$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Change $0.25$ into a fraction.

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Step 2.1

Multiply by $\frac{100}{100}$ to remove the decimal.

$y = \frac{100 \cdot 0.25}{100} x + 25$

Step 2.2

Multiply $100$ by $0.25$ .

$y = \frac{25}{100} x + 25$

Step 2.3

Cancel the common factor of $25$ and $100$ .

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Step 2.3.1

Factor $25$ out of $25$ .

$y = \frac{25 (1)}{100} x + 25$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $25$ out of $100$ .

$y = \frac{25 \cdot 1}{25 \cdot 4} x + 25$

Step 2.3.2.2

Cancel the common factor.

$y = \frac{25 \cdot 1}{25 \cdot 4} x + 25$

Step 2.3.2.3

Rewrite the expression.

$y = \frac{1}{4} x + 25$

Step 3

Multiply both sides by $4$ .

$4 y = 4 (\frac{1}{4} x + 25)$

Step 4

Simplify the right side.

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Step 4.1

Simplify $4 (\frac{1}{4} x + 25)$ .

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Step 4.1.1

Combine $\frac{1}{4}$ and $x$ .

$4 y = 4 (\frac{x}{4} + 25)$

Step 4.1.2

Apply the distributive property.

$4 y = 4 \frac{x}{4} + 4 \cdot 25$

Step 4.1.3

Cancel the common factor of $4$ .

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Step 4.1.3.1

Cancel the common factor.

$4 y = 4 \frac{x}{4} + 4 \cdot 25$

Step 4.1.3.2

Rewrite the expression.

$4 y = x + 4 \cdot 25$

Step 4.1.4

Multiply $4$ by $25$ .

$4 y = x + 100$

Step 5

Rewrite the equation.

$x + 100 = 4 y$

Step 6

Move all terms containing variables to the left side of the equation.

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Step 6.1

Subtract $4 y$ from both sides of the equation.

$x + 100 - 4 y = 0$

Step 6.2

Move $100$ .

$x - 4 y + 100 = 0$

Step 7

Subtract $100$ from both sides of the equation.

$x - 4 y = - 100$

Step 8